Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D5×Q16 |
| Fitting | C52×Q16 ⋊ C2 |
| Sylow | C52 ⋊ C2×Q16 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#64908, C5×#64910, #13100192, … |
| maximal normal subgroup of | C5×#64908, C5×#64910, #13100192, … |
| maximal quotient of | C5×#65081, C5×#65083, C5×#65082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 810);